Well, I wouldn't say PS4 does gaming better. Graphical differences have proven insignificant so far. The lower price is a big plus, though the whole reason why the One is more expensive is because it comes with the Kinect and a better headset, something the PS4 package doesn't have an answer to. So it's not as if your only getting a slightly inferior machine for that price, your also getting more in the package. For whatever that's worth, anyway. I've yet to use the Kinect camera for gaming, so I'm not going to defend it's inclusion.
Really, in terms of functionality, the one place where PS4 has One beat is in how the installations work. When you buy a game on the PS4, it'll sometimes be made available instantly, and the longest I've ever waited for an installation is about 15 minutes? On One? When I first got it it took an hour before it would let me play Ryse. I don't know if it was the slow connection or what, but it should NEVER take a disc based game that long to FULLY install, let alone get to 21% and become fully playable.
PS4 also has superior social functions....probably....I never really use them so I can't really comment on that. Also why I'm not commenting on the merits of Kinect 2.0
In the end, I really only have two recommendations when it comes to getting into the next gen:
1. Don't do it now. It's not worth it. Most of the current library for both systems are available on the current generation of systems, and I know there are at least a couple big name games coming that our cross gen. Infamous Second Son led me back to using my PS4 for about a week, and now I've done everything there is to do and the system is back to gathering dust. These systems are NOT currently worth full price, and by the time they are they will probably be a lot cheaper. At least wait until the holiday season when we have games like Arkham Knight coming.
2. If you've got the money to burn, your better of spending it on games for consoles you already own. I'm sure there are plenty of hidden gems out there that you haven't bought yet. Research some reviews, play some demos. If you don't own some of the older systems like PS3, Xbox 360, 3DS, or Vita, they are each infinitely more valuable and worthwhile purchases then any of the next gen consoles right now.